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Make a set of numbers that use all the digits from 1 to 9, once and
once only. Add them up. The result is divisible by 9. Add each of
the digits in the new number. What is their sum? Now try some other
possibilities for yourself!

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

Oh! Hidden Inside?

Stage: 3 Challenge Level:

The solution is based on the divisors of 24.

i.e 1 x 2 x 3 x 4 x 6 x 8 x 12 x 24 = 331776

Alison
at Maidstone Girls Grammar School arrived at her
solutionby trial and
improvement techniques and had found that the divisors of 30 were
too big when multiplied together and the divisors of 20 too small.
She had ascertained that 24 did have quite a lot of divisors
compared to others in this range.

Serendipity helped Ashley and John from the
Simon Langton Grammar School who "luckily chose the right number
(24)" .But, when
using prime factors, they found that 24 = 2 x 2 x 2 x 3 and they
noticed that numbers whose prime factors are of the form a x a x a
x b have ONLY 8 divisors as they showed in a multiplication table,
reproduced below:

x

1

a

aa

aaa

1

1

a

aa

aaa

b

b

ab

aab

aaab

To find the answer is then just a
matter of substituting different prime numbers for a and b
.

Similarly Robert (Smithdon High School) had
relied upon the prime factorisation of 331776 for his
solution.

Gareth
rom Hethersett High School, Norwich used algebra and found the
fourth root of 331776, namely 24 - sort of hidden
inside:

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NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.